Changes

User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 03:36, 13 February 2009

60 bytes removed , 03:36, 13 February 2009

→‎Fact 2.3

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} :R11a

::

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F2.3b. {DerR} : SxI �> B

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F2.3b. {DerR} : SxI -> B

:

{DerR}(x, y) = [ Conj(o C O)

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|- style="height:100px"

|  

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| valign="top" | <math>\operatorname{F2.2a.}</math>

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| valign="top" | <math>\operatorname{F2.3a.}</math>

| valign="top" |

<math>\begin{array}{cccl}

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& & \} & \\

\end{array}</math>

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.2a~:~R11a}</math>

+

| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3a~:~R11a}</math>

|- style="height:20px"

| colspan="3" |  

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|- style="height:100px"

|  

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| valign="top" | <math>\operatorname{F2.2b.}</math>

+

| valign="top" | <math>\operatorname{F2.3b.}</math>

| valign="top" |

<math>\begin{array}{ccccl}

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& & \downharpoonright & & \\

\end{array}</math>

−

| style="border-left:1px solid black; text-align:center" |

+

| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3b~:~R11d}</math>

−

<math>\operatorname{F2.2b~:~~~R11b~~}</math>

|- style="height:20px"

| colspan="3" |  

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|- style="height:100px"

|  

−

| valign="top" | <math>\operatorname{F2.2c.}</math>

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| valign="top" | <math>\operatorname{F2.3c.}</math>

| valign="top" |

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<math>\begin{array}{~~cccl~~}

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<math>\begin{array}{ccccl}

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\upharpoonleft \operatorname{Der}^L \upharpoonright

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\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)

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& = & \{ ~~& (x, y, z)~~ \in S \~~times I \times \underline\mathbb~~{B} ~~~:~ z =~~ \\

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& = & \underset{o \in O}{\operatorname{Conj}} \\

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& & & \begin{array}{~~cccl~~}

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& & & \begin{array}{ccl}

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\downharpoonleft ~~& \underset{o \in O}{\operatorname{Conj}} \\~~

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\downharpoonleft & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\

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& & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\

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& = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\

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& & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\

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& ) & \\

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& & ) & \\

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\downharpoonright & & \\

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\downharpoonright & & \\

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\end{array} \\

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\end{array} \\

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& & & \\

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& & \} & \\

\end{array}</math>

−

| style="border-left:1px solid black; text-align:center" |

+

| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3c~:~Log}</math>

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<math>\operatorname{F2.2c~:~~~R11c~~}</math>

|- style="height:20px"

| colspan="3" |  

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|- style="height:100px"

|  

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| valign="top" | <math>\operatorname{F2.2d.}</math>

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| valign="top" | <math>\operatorname{F2.3d.}</math>

| valign="top" |

<math>\begin{array}{cccl}

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& & \} & \\

\end{array}</math>

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| style="border-left:1px solid black; text-align:center" |

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3d~:~Def}</math>

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<math>\operatorname{F2.2d~:~~~Log~~}</math>

|- style="height:20px"

| colspan="3" |  

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|- style="height:100px"

|  

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| valign="top" | <math>\operatorname{F2.2e.}</math>

+

| valign="top" | <math>\operatorname{F2.3e.}</math>

| valign="top" |

<math>\begin{array}{cccl}

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\end{array}</math>

| style="border-left:1px solid black; text-align:center" |

−

<math>\operatorname{F2.2e~:~Log}</math>

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<math>\operatorname{F2.3e~:~Log}</math>

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<math>\operatorname{F2.3e~:~D10b}</math>

|- style="height:20px"

| colspan="3" |  

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& & \} & \\

\end{array}</math>

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| style="border-left:1px solid black; text-align:center" |

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3f~:~D10a}</math>

−

<math>\operatorname{F2.2f~:~$~}</math>

|}

Jon Awbrey

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